3 3 - 4 0 Intersection of Events These exercises involve the probability of the intersection of events.

A drawer contains an unorganized collection of 18 socks. Three pairs are red, two pairs are white, and four pairs are black.

(a) If one sock is drawn at random from the drawer, what is the probability that it is red?

(b) Once a sock is drawn and discovered to be red, what is the probability of drawing another red sock next to make a matching pair?

(c) If two socks are drawn from the drawer at the same time, what is the probability that both are red?

(a)

To find:

The probability of drawing a red sock from the drawer.

Given:

The drawer contains an unorganized collection of 18 socks out of which three pairs are red, two pairs are white, and four pairs are black.

One sock is drawn from the drawer.

Approach:

p(E)=n(E)n(S) …(1)

Here, p(E) is the probability of an event, n(E) is the number of favorable outcomes of an event, and n(S) is the set of all possible outcomes of an event.

Calculation:

There are 3 pairs of red socks, 2 pairs of white socks, and 4 pairs of black socks which implies that there are 6 red socks, 4 white socks, and 8 black socks, each pair consists of 2.

n(R)=6

Here, n(R) is the total number of red socks

(b)

To find:

The probability of drawing another red sock to make a matching pair.

(c)

To find:

The probability of drawing two red socks at the same time.